Flexibility among agents within a swarm in response to internal and external changes
is an important aspect of their collective utility.
Swarms should be able to react to quality factors in the environment, such as
the quality or safety of locations within the arena, while also not changing
their behavior in response to every fluctuation in the external environment
(resistivity). Many works on flexibility compare the performance of swarm
control algorithms under environmental conditions different than their
development [1]}, [2]}, [3]}. However, the resultant claims
of flexibility due to performance similarity across scenarios is strictly
qualitative, due to a lack of mathematical quantification of “difference” in
scenario conditions as a factor in performance comparisons. Building on the
mathematical curve similarity methods from Jekel et al. [4]}, who
tested different mathematical curve similarity measures in various noise and
normalization conditions, and the above intuition, we derive a temporally-aware
measure quantifying the difference between expected and observed performance in
arbitrary environmental conditions, and use it to quantify swarm reactivity
and adaptability in ssec:meas-flexibility.
